1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
|
#pragma once
#include "../base/base.hpp"
#include "../base/assert.hpp"
#include "../std/cmath.hpp"
#include "../std/limits.hpp"
#include "../std/type_traits.hpp"
#include <boost/integer.hpp>
namespace my
{
template <typename T> inline T Abs(T x)
{
return (x < 0 ? -x : x);
}
// Compare floats or doubles for almost equality.
// maxULPs - number of closest floating point values that are considered equal.
// Infinity is treated as almost equal to the largest possible floating point values.
// NaN produces undefined result.
// See http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm for details.
template <typename FloatT> bool AlmostEqual(FloatT x, FloatT y, unsigned int maxULPs = 256)
{
STATIC_ASSERT(is_floating_point<FloatT>::value);
STATIC_ASSERT(numeric_limits<FloatT>::is_iec559);
STATIC_ASSERT(!numeric_limits<FloatT>::is_exact);
STATIC_ASSERT(!numeric_limits<FloatT>::is_integer);
// Make sure maxUlps is non-negative and small enough that the
// default NAN won't compare as equal to anything.
ASSERT_LESS(maxULPs, 4 * 1024 * 1024, ());
int const bits = 8 * sizeof(FloatT);
typedef typename boost::int_t<bits>::exact IntType;
typedef typename boost::uint_t<bits>::exact UIntType;
IntType xInt = *reinterpret_cast<IntType const *>(&x);
IntType yInt = *reinterpret_cast<IntType const *>(&y);
// Make xInt and yInt lexicographically ordered as a twos-complement int
IntType const highestBit = IntType(1) << (bits - 1);
if (xInt < 0)
xInt = highestBit - xInt;
if (yInt < 0)
yInt = highestBit - yInt;
UIntType const diff = Abs(xInt - yInt);
return (diff <= maxULPs);
}
template <typename TFloat> inline TFloat DegToRad(TFloat deg)
{
return deg * TFloat(math::pi) / TFloat(180);
}
template <typename TFloat> inline TFloat RadToDeg(TFloat rad)
{
return rad * TFloat(180) / TFloat(math::pi);
}
template <typename T> inline T id(T const & x)
{
return x;
}
template <typename T> inline T sq(T const & x)
{
return x * x;
}
template <typename T, typename TMin, typename TMax>
inline T clamp(T x, TMin xmin, TMax xmax)
{
if (x > xmax)
return xmax;
if (x < xmin)
return xmin;
return x;
}
template <typename T> inline bool between_s(T a, T b, T x)
{
return (a <= x && x <= b);
}
template <typename T> inline bool between_i(T a, T b, T x)
{
return (a < x && x < b);
}
inline int rounds(double x)
{
return (x > 0.0 ? int(x + 0.5) : int(x - 0.5));
}
inline size_t SizeAligned(size_t size, size_t align)
{
// static_cast .
return size + (static_cast<size_t>(-static_cast<ptrdiff_t>(size)) & (align - 1));
}
template <typename T>
bool IsIntersect(T const & x0, T const & x1, T const & x2, T const & x3)
{
return !((x1 < x2) || (x3 < x0));
}
template <typename T>
void Merge(T const & x0, T const & x1, T const & x2, T const & x3, T & x4, T & x5)
{
ASSERT(IsIntersect(x0, x1, x2, x3), ());
x4 = min(x0, x2);
x5 = max(x3, x1);
}
template <typename T>
size_t MergeSorted(T const * a, size_t as, T const * b, size_t bs, T * c, size_t cs)
{
T const * arrs [] = {a, b};
size_t sizes[] = {as, bs};
size_t idx[] = {0, 0};
int i = 0;
int j = 1;
int k = 0;
if ((sizes[i] == 0) && (sizes[j] == 0))
return 0;
if ((sizes[i] == 0) && (sizes[j] != 0))
swap(i, j);
while (true)
{
/// selecting start of new interval
if ((idx[j] != sizes[j]) && (arrs[i][idx[i]] > arrs[j][idx[j]]))
swap(i, j);
c[k] = arrs[i][idx[i]];
c[k + 1] = arrs[i][idx[i] + 1];
idx[i] += 2;
while (true)
{
if (idx[j] == sizes[j])
break;
bool merged = false;
while (IsIntersect(c[k], c[k + 1], arrs[j][idx[j]], arrs[j][idx[j] + 1]))
{
merged = true;
Merge(c[k], c[k + 1], arrs[j][idx[j]], arrs[j][idx[j] + 1], c[k], c[k + 1]);
idx[j] += 2;
if (idx[j] == sizes[j])
break;
}
if (!merged)
break;
swap(i, j);
}
/// here idx[i] and idx[j] should point to intervals that
/// aren't overlapping c[k], c[k + 1]
k += 2;
if ((idx[i] == sizes[i]) && (idx[j] == sizes[j]))
break;
if (idx[i] == sizes[i])
swap(i, j);
}
return k;
}
// Computes x^n.
template <typename T> inline T PowUint(T x, uint64_t n)
{
T res = 1;
for (T t = x; n > 0; n >>= 1, t *= t)
if (n & 1)
res *= t;
return res;
}
template <typename T> inline T NextModN(T x, T n)
{
return x + 1 == n ? 0 : x + 1;
}
template <typename T> inline T PrevModN(T x, T n)
{
return x == 0 ? n - 1 : x - 1;
}
}
|
